Hi rubberball!
For big aircraft you have a graph in which knowing your take off weight and trip distance you find the optimum altitude for the short hops, which differs from the optimum altitude.
For long trips you have optimum altitude charts for a given weight and atmospheric conditions. Normally as you burn fuel and become lighter you climb to the new optimum altitude in such long flights as EGLL-KLAX ones (and even in shorter ones).
Transition altitude is the altitude where you have to change your altimeter setting from standard (1013 milibars or 29.92 inHg) to the local altimeter setting (in your videos you may hear QNH, and it's the actual pressure the airfield may had if it was at sea level, or QFE if it's the actual air pressure at the airfield). It's purpose is to have an accurate altimeter reading near ground.
The safe altitude around an airport is MSA (Minimum Sector Altitude), which is published in the charts, and guaratees a 1000' obstacle clearance within 25NM from a navaid (usually in the airport or very close). You can have from just one MSA to up to normally 4-5 for different sectors. Its like when you cut a round cake in pieces.
Hope that you understand this terms and please feel welcome to ask whatever you want.
Regards,
Pablo